Secure and Flexible Coded Distributed Matrix Multiplication Based on Edge Computing for Industrial Metaverse

The Industrial Metaverse is driving a new revolution wave for smart manufacturing domain by reproducing the real industrial environment in a virtual space. Real-time synchronization and rendering of all industrial factors result in numerous time-sensitive and computation-intensive tasks, especially matrix multiplication. Distributed edge computing (DEC) can be exploited to handle these tasks due to its low-latency and powerful computing. In this paper, we propose an efficient and reliable coded DEC framework to compute large-scale matrix multiplication tasks. However, an existence of stragglers causes high computation latency that seriously limits the application of DEC in the Industrial Metaverse. To mitigate the impact of stragglers, we design a secure and flexible PolyDot (SFPD) code, which enables information theoretic security (ITS) protection. Several improvements can be achieved with the proposed SFPD. First, it can achieve a smaller recovery threshold than that of the existing codes in almost all settings. And compared with the original PolyDot codes, our SFPD code considers the extra workers required to add ITS protection. It also provides a flexible tradeoff between recovery threshold and communication & computation loads by simply adjusting two given storage parameters $p$ and $t$. Furthermore, as an important application scenario, the SFPD code is employed to secure model training in machine learning, which can alleviate the straggler effects and protect ITS of raw data. The experiments demonstrate that the SFPD code can significantly speed up the training process while providing ITS of data. Finally, we provide comprehensive performance analysis which shows the superiority of the SFPD code.